Max Tegmark's infinite universes

[drkitten]

Penrose is a poor analogy. Penrose's book about AI is not within his area of expertise which is mathematics. Tegmark is a cosmologist writing about cosmology. So, you offer no scientific support for your hostility for Tegmark's theories; instead you continue your emotional bluster about "lucky charms," which is of little value.

... but still of greater value than the entire corpus of supporting evidence for Tegmark's multiverse theories, which is of zero value.

Your entire argument in support of Tegmark boils down to "we can't rule it out."

Which is true. But since there are an infinite number of wrong things which we can't rule out as well, that hardly puts Tegamark's theories in particularly good company.

 

[Paul C. Anagnostopoulos]

Which isn't surprising, since his infinite universe theory is a nutcase theory that no sensible physicist takes at all seriously.

Are you talking about the multiverse theory?

I'll go for multiverse based on Occam alone.

~~ Paul

 

[drkitten]

Are you talking about the multiverse theory?

No, Tegmark goes far beyond the multiverse theory, which is part of what makes him a nutcase. The defining principle of his theory is that everything concievable exists somewhere, or more formally, "all structures that exist mathematically exist also physically."

Which means that somewhere there is a universe that consists solely of Royal Daulton figurines except for the exact center, which is a torus four km in circumference and made of caramel nougat.

It also means that, somewhere, there is a universe that looks exactly like ours, except that at a point a little over a year from now, everything in it will spontaneously turn into a giant bowl of Lucky Charms.

I am entirely serious here.

Perpetual Student, quite correctly, mocks my Lucky Charm universe as being utterly implausible. What he (and calvert) don't seem to realize is that the Lucky Charm universe is a direct consequency of Tegmark's theories. If Tegmark's theories are true, so is the Lucky Charm universe theory. Along with the related Count Chocula universe theory, the Rice Krispie Treat universe theory, and the ever popular Vegemite on toast universe theory.

And, again, I'm being entirely serious here. Anything you can describe in noncontradictory fashion exists somewhere in Tegmark's multiverse.

Tegmark's universe is therefore less plausible than the Lucky Charms universe, by simple probability theory. As Tegmark's universe implies the Lucky Charms universe, this is a simple observation that A&B is less probable than either A or B alone. Tegmark's universe is less plausible than the Lucky Charms universe and the Count Chocula universe combined.

Which makes "bonkers" far too kind a word to describe it,.... but forum rules prevent a fuller and more complete description. I lack sufficient ridicule to hold it up to.

 

[Fnord]

What possible practical value would there be in settling the discussion one way or the other?

Jus' askin'...

 

[Apathia]

Calvert,

I have no comment on Tegmark, as I'm not familiar with his views at all.
As far as Repetition of the philisophical or the comological sort,
I think DrKitten correctly pointed out that infinity doesn't necessarily involve repetition.

Infinity is a subtler concept than the popular usage of the word.
An Infinite universe could be bounded or unbounded.
I don't know what the current evidence leans to on this.
But I'm not afraid that I'll have to redo my failed relationships over again with the same disasterous results.

Age wise you and I could have been in college at the same time, but the Calvert I remember was a tad younger than I.
It's just that I rarely run into the name, Calvert.
And this my just be your screen name.

 

[Apathia]

No, Tegmark goes far beyond the multiverse theory, which is part of what makes him a nutcase. The defining principle of his theory is that everything concievable exists somewhere, or more formally, "all structures that exist mathematically exist also physically."

Which means that somewhere there is a universe that consists solely of Royal Daulton figurines except for the exact center, which is a torus four km in circumference and made of caramel nougat.

It also means that, somewhere, there is a universe that looks exactly like ours, except that at a point a little over a year from now, everything in it will spontaneously turn into a giant bowl of Lucky Charms.

I am entirely serious here.

Wow!
If this circus holds then there are countless universes in which I never met Gale S. and she's a bowl of Lucky Charms!
It's an amusingly comforting idea.
If only she'd had all those pink hearts!

 

[Paul C. Anagnostopoulos]

Tegmark's universe is therefore less plausible than the Lucky Charms universe, by simple probability theory. As Tegmark's universe implies the Lucky Charms universe, this is a simple observation that A&B is less probable than either A or B alone. Tegmark's universe is less plausible thatn the Lucky Charms universe and the Count Chocula universe combined.

Is this the case when the sample space is infinite?

Edited to add: I guess it has something to do with the probability distribution within the infinite sample space. Isn't there something about there not being a uniform probability distribution over an infinite space?

By the way, does he propose a countable or uncountable infinity of universes? Wait, Godel has something to say about that, no?



~~ Paul

 

[drkitten]

Is this the case when the sample space is infinite?

Yes. Consider the probability of picking a real number in [0,1) uniformly at random. The probability of picking a real number that is less than 0.2 is greater than the probability of picking a real number that is less than 0.2 but more than 0.15.

Edited to add: I guess it has something to do with the probability distribution within the infinite sample space. Isn't there something about there not being a uniform probability distribution over an infinite space?

Not quite. There is indeed a uniform probability distribution over an uncountably infinite space -- and although there is no uniform probability distribution within a countably infinite space, that doesn't seem relevant to Tegmark's theories.

 

[SezMe]

As far as Repetition of the philisophical or the comological sort, I think DrKitten correctly pointed out that infinity doesn't necessarily involve repetition.

It does for all states with a non-zero probability .

 

[Apathia]

It does for all states with a non-zero probability .

I see. If it can happen, it will happen again.

 

[Paul C. Anagnostopoulos]

Yes. Consider the probability of picking a real number in [0,1) uniformly at random. The probability of picking a real number that is less than 0.2 is greater than the probability of picking a real number that is less than 0.2 but more than 0.15.

Indeed. But somehow this example doesn't seem relevant to an infinity of universes. A better example might be the probability of picking at random a real number containing 94758 vs. picking one containing both 94758 and 029534857. Is the second probability lower?

Not quite. There is indeed a uniform probability distribution over an uncountably infinite space -- and although there is no uniform probability distribution within a countably infinite space, that doesn't seem relevant to Tegmark's theories.

From http://space.mit.edu/home/tegmark/multiverse.html:

Is there a countable or uncountable infinity of universes?

Q: In your calculation of the average distance between you and another copy of you, did you take into account the uncertainty principle and its effect on the number of possible states? I've always explained away "copies" of myself by saying that the Universe may be infinite in size, but *countably infinite*. The number of possible states is *uncountably infinite*, on the other hand.... so any particular state only occurs once, on average.

A: Let's first ignore the important complication of past history and ask how many physically distinct states N there are in a volume V. In classical physics, N is infinite (indeed uncountably infinite) as you say, since even specifying the position of a single particle requires infinitely many decimals. In quantum mechanics, however, N is finite: if the temperature never exceeds T, we of course have N < ln S, where S is the entropy of the thermal state with temperature T (I'm taking Bolzmann's constant k=1). Interestingly, the number of states appears to be finite even when taking general relativity into account, which is closely related to the holographic principle: the entropy is maximized if all the matter in V is in a single black hole, in which case, as you know, the Bekenstein-Hawking formula says that N is of order the surface area measured in Planck units. So yes, I see your reasoning, and find it quite striking that quantum mechanics, uncertainty principle and all, contrary to what one might expect, gives fewer states than classical physics. In the limit V->oo, quantum mechanics therefore gives a countable rather than uncountable infinity of states.

~~ Paul

 

[shemp]

I see. If it can happen, it will happen again.

Indeed. Here's an example from a groundbreaking case study:

 

[drkitten]

It does for all states with a non-zero probability .

No.

Consider the infinite sequence 0.143333333333333333333......

Or more generally, consider any non-ergodic sequence.

The probability of a 4 is demonstrably non-zero (it's right there, see?) but it will never recur in that sequence.

Not all infinite sequences are ergodic, although I suspect that "almost all" of them are.

 

[drkitten]

Indeed. But somehow this example doesn't seem relevant to an infinity of universes. A better example might be the probability of picking at random a real number containing 94758 vs. picking one containing both 94758 and 029534857. Is the second probability lower?

Yes. Consider the real number 0.94758000000000000000.... Or 0.0947580000000...... Or 0.94758888888....., or 0.947589475894758(94758)....

All of these numbers are in set 1, but not set 2. Since set 2 is a proper subset of set 1, the probability of a number being in set 2 is less than the probability of being in set 1.

Of course, actually calculating those probabilities will be a bear, and you're likely to find that the difference is literally infinitesimal.

 

[calvert]

Refering to many above replies.

Much of what you are debating has been addressed by Tegmark on his web site. The following link is to a section of FAQs-- Goggle Tegmark +FAQ. The referenced site should come up at the top. At the top of the first page their should be a link to his FAQ section.

drkitten you continue to use examples of universes made up of cereal. What you are doing is taking almost certainly examples of the least probable cases. Yet you have said that because something is infinite it does not infer that all possibilities must be included. In the vast majority of universes I may exist in I don't go out of my way to hit the squirrel. As you correctly state a number such as 1/3 has an infinite solution, i.e. 0.3333333333------------ and yet no integers other than 3. Could there be a Lucky Charm universe. Possibly, although my guess is that it would violate so many physical laws that it would fall into the "anything that can't happen,won't happen" category.

Also, you keep saying that Tegmark has no evidence for any of his "nutcase" theory. He has plenty of evidence, some hard evidence such as the CMB indicating a flat universe. Thus a minimum of approx. 1000 hubble volumes must be present to explain the data. Also, much mathmatical evidence. His Level 3 mutiverse is taken directly from Everett's model. This mutiverse view has become widely accepted in the scientific community (Guth, Linde, Vilenkin) because it offers explanation for a host of previous inconsistencies requiring added factors and constants. Inflation, QM, and String Theory all depend on the existence of parallel universes. On the other hand there is absolutely no hard evidence to support the Copenhagen Model.

To All:

My original question still is hanging out there. Let's be kind and say it is given that there are an infinite number of universes and that we populate a large number. Also, that big bangs occur infinitely beginning new universe trees. I have read no where of the possibility of repetitions spanning huge differences in time. If we assume my above statements would it not be possible that I have written this e-mail a billion or trillion years ago. Obviously every repetition will not be in time sync with us.

 

[Paul C. Anagnostopoulos]

Of course, actually calculating those probabilities will be a bear, and you're likely to find that the difference is literally infinitesimal.

And so perhaps Tegmark is only infinitesimally over the top.

~~ Paul

 

[SezMe]

No.

Consider the infinite sequence 0.143333333333333333333......

No.

If you sequence is DEFINED as one where only one 4 can occur then the probability of another one occurring is zero, which does NOT contradict my statement.

 

[drkitten]

drkitten you continue to use examples of universes made up of cereal. What you are doing is taking almost certainly examples of the least probable cases. Yet you have said that because something is infinite it does not infer that all possibilities must be included.

That is correct.

And it is precisely because Tegmark claims, in the teeth of the evidence, that in an infinite space, every possibility must be included, that he is wrong.

If his claim was merely that "there are probably a lot of universes, so there's probably a lot of wierd stuff out there," it would merely be speculative.

It's when he goes from "there are a lot of univerese, therefore every conceivable type of wierd stuff out there" that he crosses the border into "bonkers."

For two reasons. First, the multiverse is as yet unproven. Second and more importantly, infinity doesn't work the way he thinks it does.

Could there be a Lucky Charm universe. Possibly,

And that's exactly what's wrong with Tegmark's theory. "Possibly" isn't an answer. Everything is either "impossible" or "exists."

although my guess is that it would violate so many physical laws that it would fall into the "anything that can't happen,won't happen" category.

No. No physical laws would be violated. Heisenberg just says that such an event would be really really unlikely. But since it's possible, Tegmark says it's happening.

 

[drkitten]

No.

If you sequence is DEFINED as one where only one 4 can occur then the probability of another one occurring is zero, which does NOT contradict my statement.

Re-read my posting and consider general non-ergodic sequences.

 

[calvert]

Possibly????

Having been a research scientist for close to 40 years one thing I can say with certainty is that Possibly is by far the most frequent result one gets when running an experiment to test any hypothesis. Possibly is a good result. One confirmed no puts you out of business. Yes, only means that the next experiment may be NO. Will Newton's apple always fall to the ground? Is gravity as we know it proven? Can you walk through a wall, possibly?